Method and apparatus for reconstruction calibration of detector position and source motion based on a multi-pin phantom

ABSTRACT

Certain embodiments relate to a method and apparatus for calibrating an imaging system having an array of detector elements arranged with respect to a reference position and having an energy source moving in a pattern to irradiate the array of detector elements. The method includes initiating estimated detector positions for the array of detector elements and an estimated motion pattern for the energy source. The estimated detector positions and motion pattern are defined with respect to a reference position in the imaging system. The method further includes scanning a phantom having pins located at positions in the phantom and calculating estimated pin positions, with respect to the reference position, based on at least one of the estimated detector positions and motion pattern. The method further includes modifying at least one of the estimated detector positions and motion pattern based on at least two of the estimated detector positions, motion pattern and pin positions.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application relates to, and claims priority from, co-pendingapplication Ser. No. 10/065,700 filed on the same date as the presentapplication and entitled “Method and Apparatus for Controlling ElectronBeam Motion Based on Calibration Information”. The present applicationrelates to, and claims priority from, U.S. Provisional Application No.60/359,562, filed on Feb. 25, 2002, and entitled “High-PrecisionMeasurement of Projection Geometry for CT Using a Low-Precision MultipinPhantom”. The provisional application names Erik Chell and John Couch asjoint inventors, and the co-pending application names Erik Chell, JohnCouch, and Paul Magnuson as joint inventors. The co-pending andprovisional applications are incorporated by reference herein in theirentirety including the specifications, drawings, claims, abstracts andthe like.

BACKGROUND OF INVENTION

The present invention generally relates to calibration of a medicaldiagnostic imaging system. In particular, the present invention relatesto reconstruction calibration of detector position and source motionbased on a multi-pin phantom.

Medical diagnostic imaging systems encompass a variety of imagingmodalities, such as x-ray systems, computerized tomography (CT) systems,ultrasound systems, electron beam tomography (EBT) systems, magneticresonance (MR) systems, and the like. Medical diagnostic imaging systemsgenerate images of an object, such as a patient, for example, throughexposure to an energy source, such as x-rays passing through a patient,for example. The generated images may be used for many purposes. Forinstance, internal defects in an object may be detected. Additionally,changes in internal structure or alignment may be determined. Fluid flowwithin an object may also be represented. Furthermore, the image mayshow the presence or absence of items in an object. The informationgained from medical diagnostic imaging has applications in many fields,including medicine and manufacturing.

In order to help ensure that medical diagnostic images are reliable, itis advantageous to calibrate medical diagnostic imaging systems. Thecalibration of imaging systems is important for several reasons,including image quality and system performance. Poor image quality mayprevent reliable analysis of an image. For example, a decrease in imagecontrast quality may yield an image that is not usable clinically. Thecalibration of medical imaging systems may help to produce a distinctand usable representation of an object.

The calibration of medical diagnostic systems is also important forsafety reasons. For example, exposure to excessively high levels ofx-ray energy may create certain health risk. Because of the health risk,governmental standards have been established for the use of x-raysystems. The level of x-ray energy emitted by an x-ray system may bemeasured in terms of radiation dosage. Calibration of x-ray systems andother medical diagnostic imaging systems may ensure that the radiationdosage to which the target is exposed does not exceed clinicalstandards.

One device that may be used in the calibration of medical diagnosticimaging system parameters, such as image quality and radiation dosage,is called a phantom. Many types of phantoms have been proposed. Forexample, phantoms may be physical replicas of imaging targets, such ashuman body parts. Another example of a phantom type is a physics-basedphantom. A physics-based phantom may be comprised of various structuresaffixed to a common base. The structures of a physics-based phantom maypossess varying characteristics, such as shape, size, density,composition, and arrangement, for example. Furthermore, physics-basedphantoms may be constructed from various materials, including metal andplastic.

The structures of physics-based phantoms may affect characteristics ofenergy sources, such as x-rays, for example, which pass through thephysics-based phantom. For example, metal structures may block x-rays.Additionally, plastic structures may merely decrease the energy level ofreceived x-rays. A pattern resulting from the changes in the energylevels of received x-rays is represented in an x-ray image. Theresulting pattern in the x-ray image may be easy to detect and analyzedue to factors such as the contrast produced by the difference inreceived x-ray energy levels.

Phantoms may serve a variety of purposes. For example, phantoms may beused to practice positioning of an imaging target. Additionally,phantoms may be used to test parameters of the medical imaging system.Also, phantoms may be used to gauge the radiation dosage of energyemitted by the medical diagnostic imaging system. Furthermore, phantomsmay be used for calibration and image quality assessment. However, foraccurate positioning and system calibration, conventional phantoms areexpensive and require high precision during manufacture. Thus, there isa need for a phantom that may accurately and easily determine componentpositions in a medical diagnostic imaging system. There is a need for aninexpensive phantom that may be used to calibrate a medical diagnosticimaging system which does not require high precision during manufactureor use.

In CT imaging systems, for example, an object such as a patient or aphantom is illuminated with x-rays from a plurality of angles to producea set of x-ray projections. Each of the plurality of detectors in theimaging system samples the x-ray signal a plurality of times, and whenthe aggregate data from each detector is assembled with sample number onone axis and detector number on the other, the result is referred to asa sinogram. For example, if there are 1728 detectors in a CT system andeach detector is sampled 864 times, the sinogram would be a matrix of864×1728 x-ray attenuation values. The term “sinogram” derives from thesinusoidal shadow a solid object like a pin presents. The CT imagingsystem calculates or “reconstructs” a two dimensional image data fromthe sinogram data.

Inaccuracies in the CT imaging system may result in blurring, streaking,or introduction of ghost images or artifacts in the resulting image. Forexample, if a detector position or the center of a medical imagingsystem is inaccurate, an x-ray will be projected at an incorrect angleand produce an error in the resulting image. Thus, a need exists for amethod and apparatus for more accurate calibration of a medicaldiagnostic imaging system.

Current calibration methods often involve time intensive or complicatedprocedures. Frequent calibration is required to help ensure consistentimage quality. Additionally, existing calibration methods rely on theassumption that system components, such as detectors, have beenaccurately positioned and located. That is, conventional systems rely onthe manufacturer's stated position of detectors and energy beam sourcein relation to the center of the imaging system. Accuracy may be timeconsuming and difficult to achieve, and error in the manufacturer'spositioning may result in streaks on the images. Furthermore, currentcalibration methods require precise positioning of the phantom in orderto properly calibrate the imaging system. Thus, a need exists for amethod and apparatus for quick and easy system calibration. A needfurther exists for imaging system calibration using a low-precisionphantom.

Additionally, EBT systems utilize a high energy beam of electrons tostrike a target and produce x-rays for irradiating an object to beimaged. The point where the electrons strike the target is called the“beam spot”. Dipole, quadrupole, and focusing coils may be used todeflect the electrons along the target to produce x-rays. Motion of theelectron beam must be “tuned” to optimize beam motion and moreaccurately produce a beam spot.

Current methods of tuning EBT scanners involve sweeping the electronbeam over “w” shaped wires (“W-wires”) and evaluating the beam spotshape and position as a function of time. W-wires are expensive,however. Thus, there is a need for an inexpensive method of “tuning” orcalibrating an electron beam. Additionally, in current EBT systems, onlya small number of W-wires may fit (for example, 15 wires in currentscanners), reducing accuracy of a tuning correction. Thus, there is aneed for a system for more accurately tuning electron beam motion.Furthermore, in current systems, the W-wires are separated from thescanning targets. Therefore, a theoretical transfer function iscurrently necessary to move the beam from the W-wire target to thescanning target. Thus, a need exists for a method of measuring tuneaccurately on the scanning target itself, rather than on W-wires. Thereis a need for direct measurement and modification of electron beamcurrents based on actual imaging x-rays.

SUMMARY OF INVENTION

Certain embodiments of the present invention relate to a method andapparatus for calibrating an imaging system. Certain embodiments relateto a method for calibrating an imaging system having an array ofdetector elements arranged with respect to a reference position andhaving an energy source moving in a pattern to irradiate the array ofdetector elements. Calibration may result in more accurate measurementof detector positions and the motion of an electron beam spot as afunction of time, which provides improved image quality to the imagingsystem. The method includes initiating estimated detector positions forthe array of detector elements and an estimated motion pattern for theenergy source. The estimated detector positions and motion pattern aredefined with respect to a reference position in the imaging system. Themethod further includes scanning a phantom including pins andcalculating estimated pin positions for the pins in the phantom, withrespect to the reference position, based on at least one of theestimated detector positions and motion pattern. The method furtherincludes modifying at least one of the estimated detector positions andmotion pattern based on at least two of the estimated detectorpositions, motion pattern and pin positions.

Certain embodiments relate to a system for improved calibration of adiagnostic imaging system. The system includes an array of detectorelements arranged with respect to a reference position, an energy sourcemoving in a pattern to irradiate the array of detector elements, aphantom including pins and a reconstruction system calculating estimatedpin positions for the pins in the phantom, with respect to the referenceposition, based on at least one of estimated detector positions andestimated motion pattern of the energy source. The reconstruction systemmodifies at least one of the estimated detector positions and motionpattern based on at least two of the estimated detector positions,motion pattern, and pin positions. In certain embodiments, thereconstruction system modifies at least one of the estimated detectorpositions and motion pattern by computing an error vector {right arrowover (E)}={right arrow over (h)}*{right arrow over (P)}, wherein Erepresents an error associated with the estimated detector positions,motion pattern and/or pin positions (the geometrical parameters), hdenotes adjustments to produce more accurate estimated detectorpositions, motion pattern and pin positions and P represents a matrix ofderivatives for detector-phantom pin samples with respect to thedetector positions, motion pattern and pin positions. The error vector Erepresents an error between empirical data in a sinogram and theoreticalvalues obtained by evaluating the geometrical parameters in a model ofthe system. Solving for the h vector and using its values to modifydetector positions, pin positions, and the beam spot motion pattern mayresult in improved knowledge of the actual geometry of the imagingsystem.

Certain embodiments relate to a multipin phantom for calibrating animaging system. The phantom includes a block for housing a plurality ofpins and a plurality of pins placed in the block to enable triangulationof detector elements of an imaging system.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 illustrates an EBT imaging system used in accordance with anembodiment of the present invention.

FIG. 2 illustrates a multipin phantom formed in accordance with anembodiment of the present invention.

FIG. 3 illustrates a flow diagram for a method for calibrating a medicaldiagnostic imaging system in accordance with an embodiment of thepresent invention.

FIG. 4 illustrates ray tracing used in accordance with an embodiment ofthe present invention.

FIG. 5 illustrates a clustering of rays analyzed with a least-squaresmethod used in accordance with an embodiment of the present invention.

FIG. 6 shows a relationship, in a one dimensional case, betweentheoretical parameter values, actual parameter values, and the amount bywhich each parameter is to be changed used in accordance with anembodiment of the present invention.

FIG. 7 illustrates an electron beam tuning system used in accordancewith an embodiment of the present invention.

FIG. 8 illustrates a flow diagram for a method for adjusting an electronbeam in accordance with an embodiment of the present invention.

The foregoing summary, as well as the following detailed description ofcertain embodiments of the present invention, will be better understoodwhen read in conjunction with the appended drawings. For the purpose ofillustrating the invention, there is shown in the drawings, certainembodiments. It should be understood, however, that the presentinvention is not limited to the arrangements and instrumentality shownin the attached drawings.

DETAILED DESCRIPTION

For the purpose of illustration only, the following detailed descriptionreferences a certain embodiment of an Electron Beam Tomography (EBT)imaging system. It is understood that the present invention may be usedwith other imaging systems (such as computed tomography systems, andother imaging systems, for example).

FIG. 1 illustrates an EBT imaging system 100 formed in accordance withan embodiment of the present invention. The system 100 includes anelectron source 110, a focusing coil 120, deflection coils 130, targetrings 140-143, a data acquisition system (DAS) 150, a reconstructionsystem 155, a detector array 160, and an object positioner 170. As willbe described further below, the electron source 110 generates anelectron beam that travels to the focusing coil 120. At the focusingcoil 120, the electron beam is focused to create a narrow, ellipticalbeam spot on the target rings 140-143. At the deflection coils 130, theelectron beam is deflected to sweep along one of the target rings140-143.

When the focused electron beam hits one of the target rings 140-143, thecontacted target rings 140-143 emit a fan beam of x-rays. The point atwhich electrons from the electron beam are deflected onto the targetring 140 is referred to as the “beam spot” and serves as a source ofimaging x-rays. In certain embodiments, there may be a single targetring 140 or a plurality of target rings 140-143, for example. In certainembodiments, the target rings 140-143 are made of tungsten. The electronbeam may be swept along a 210 degree arc to produce, at each spot alongthe arc, a fan beam of x-rays.

The x-rays emitted from the target rings 140-143 pass through theobject, such as a patient, for example, that is located on the objectpositioner 170. The object positioner 170 may be a table, a support, awall bucky, or other movable or non-movable positioner, for example. Thex-rays then impinge upon the detector array 160. The detector array 160includes at least one row of detector elements. The detector elements ofthe detector array 160 generate signals in response to the impingingx-rays. The signals are transmitted from the detector array 160 to theDAS 150. The DAS 150 collects the data and sends the data to areconstruction system 155. The reconstruction system 155 analyzes thesignals and generates a medical diagnostic image from the data obtainedfrom the detector array 160. The reconstruction system 155 may alsostore data or transmit data to an external processor or memory, forexample. The reconstruction system 155 may be embodied in softwareand/or in hardware, for example.

The detector array 160 receives x-rays from several angles, along thearc over which the beam is swept, to produce a set of x-ray projections.The projection data is received by the DAS 150, and the total data fromone sweep are arranged in a matrix called a sinogram. Within thesinogram, each row contains all projection data for one detectorelement, and each column contains data at a certain sample number forthat detector element. From the two-dimensional sinogram of projectiondata, the reconstruction system 155 may reconstruct a two-dimensionalimage, typically characterizing an axial slice of the object imaged.Backprojection or another reconstruction technique may be used toreconstruct the two-dimensional image. The resulting image, however, maycontain streaks or image artifacts (such as ghost images, for example)due to imperfections or inaccuracies in the system 100 and position ofsystem 100 components. Examples of inaccuracies include errors indetector position or mischaracterization of the motion of the beam spot.Calibration of the system 100 may help to reduce or eliminate streaks orimage artifacts to improve image quality. A phantom may be used tocalibrate the system 100 to improve image quality and accuracy, forexample.

FIG. 2 illustrates a multipin phantom 200 used for system geometricalcalibration in accordance with an embodiment of the present invention.The multipin phantom 200 includes a block 210 of foam or other similarmaterial. The multipin phantom 200 also includes a plurality of pinsplaced on or in the block 210. Multiple pins enable the phantom 200 totriangulate on system 100 components, such as the detector array 160 andthe individual detectors of the detector array 160 and electron beam,for example, and obtain additional measurements, such as radius, motion,and position, for example. In certain embodiments, the multipin phantom200 includes pins 220-227. The pins may include a metal, such astungsten, for example. The pins 220-227 are placed roughly in a circleand are aligned along an axis of the detector array 160. The pins220-227 may be enclosed in a cylinder of plastic for protection. Themultipin phantom 200 may be attached to a smaller cylinder that allowsthe multipin phantom 200 to be mounted on a centermount of the objectpositioner 170.

FIG. 3 illustrates a flow diagram 300 for a method for calibrating amedical diagnostic imaging system 100 in accordance with an embodimentof the present invention. After a brief overview, the steps of themethod will be described in further detail below. First, at step 310,positions of the elements of the detector array 160, coefficients ofenergy beam or source motion, and other manufacturer information arepreloaded. Then, at step 320, the multipin phantom 200 is placed on theobject positioner 170, and a scan is acquired. Next, at step 330,phantom pin locations are analyzed. Using the theoretical locations ofthe elements in the detector array 160 and theoretical motion of thebeam spot along the target rings 140-143, a rough estimation of thelocations of pins 220-227 in the phantom 200 is made. Then, at step 340,the positions of the pins 220-227 and the motion of the beam spot alongthe target rings 140-143 is refined in a calculation that assumes thedetector elements to be in their ideal location. At step 350, therefined pin positions and beam spot motion are used to refine thepositions of the detector elements. At step 360, a quality metric called“cluster error” (defined below) is calculated and used to decide if themeasurement of the detector element and beam spot positions issufficient. If measurement is not sufficient, refinement continues initerations of the above process.

Now the method of calibration will be described in more detail. First,at step 310, theoretical (or ideal or desired) component position datais preloaded. The theoretical data may be the expected position of thecenter of the detector array 160 and of the individual detector elementsin the detector array 160, as well as coefficients describing the radialand angular motion of the beam spot produced by the energy source 110.The preload of desired data may be preceded by a blank scan to accountfor background or noise in the EBT imaging system 100. Then, at step320, the multipin phantom 200 is scanned. The multipin phantom 200 maybe placed on the object positioner 170, without concern for the preciselocation of the multipin phantom 200.

Next, at step 330, the positions of the detectors in the detector array160 and the motion of the electron beam are “frozen” at the assumed ortheoretical values. A scan with the multipin phantom 200 is performed. Asinogram is produced from irradiation of the multipin phantom 200 byradiation, such as x-rays, for example, from the target rings 140-143.By way of example only, 864 detector elements with 864 samples each maybe included in the detector array 160, and eight pins 220-227 may beincluded in the multipin phantom 200. In this example, the sinogramobtained from the detector array 160 is an 864-by-864 sinogram.

Next, a trace of pins 220-227 through the sinogram is performed toidentify the positions of individual pins 220-227 in the sinogram. Areasof high attenuation are assumed to be pin 220-227 shadows and arecharacterized for their central points and traced through the sinogram.Pin 220-227 position overlaps and other data may also be removed. By wayof example, a sample may be obtained every 40 microseconds. The time atwhich the center of a pin 220-227 is detected may be a fractional samplenumber, such as sample number 1.25. With 864 detector elements and 8pins, the result is an 864-by-8 table of pin 220-227 samples sorted bypin number (hereinafter, pin sample table). Pins 220-227 are identifiedby a sample number that corresponds to the time at which the sample wasobtained (e.g., the time at which the center of the pin 220-227 wasobserved).

Then, at step 340, the detector array 160 position is “frozen” or heldconstant at the values calculated in step 330. New values for thecoefficients describing the motion of the beam spot on the target rings140-143 and pin 220-227 positions are refined from values obtained inprevious steps. The mathematical method of this refinement will bedescribed in detail below.

Next, at step 350, the source 110 and pin 220-227 positions are “frozen”or held constant at the values calculated in step 340, and the detectorarray 160 positions are refined. Detector position refinement proceedsin a manner similar to the pin 220-227 position refinement of step 340.In effect, pin 220-227 positions and electron beam or source 110 motionmay be used to triangulate on each detector position in the detectorarray 160.

Then, at step 360, an assessment of the self-consistency of the set ofequations describing the system 100 is made. Each entry in the pinsample table can be turned into a hypothetical ray from the detectorelement to the target ring 140-143. One end of the detector-target rayis defined by the position of the detector element, while the other isdefined by the location of the beam spot at the time that detectorelement saw the pin 220-227.

FIG. 4 illustrates a ray tracing 400 used in accordance with anembodiment of the present invention. In the ray tracing 400, a rayextends from a detector element 465 to the target ring 140. The actualposition of the pin 220 may be unknown.

After all detector-target rays for a given pin 220-227 are determined,the “centroid” of the rays is computed. The centroid is defined as aposition in space which minimizes, in a least squares sense, thedistance of closest approach of each ray to the centroid. The centroidis then assumed to be the position of the pin 220-227 for subsequentcalculations.

The least squares method is used to solve a set of equations with moreequations than unknown variables. Accordingly, the answer achieved isnot an exact solution but rather a solution that minimizes the sum ofthe squares of the residual errors.

FIG. 5 illustrates a clustering 500 of rays analyzed with aleast-squares method used in accordance with an embodiment of thepresent invention. In FIG. 5, a plurality of rays from detector elementsto the target ring 140-143 overlap to form the centroid in the region ofthe actual pin. The variation among the rays may be used to determinethe accuracy of the system of equations describing the pin positions,detector element positions, and beam motion.

Once the centroid has been determined for all pins, a “cluster error”can be calculated. It is defined as the average distance by which eachdetector-target ray misses its own centroid. In a perfect system,cluster error would be zero. In practice, a cluster error of 5 microns,for example, usually indicates a sufficiently self-consistent solutionfor streak-free images.

At step 370, if the cluster error is above a certain threshold,refinement continues for the positions of the detector elements and thepins 220-227, along with source 110 motion as a function of time.Refinement continues according to the steps described above, starting atstep 340, for example. For example, if the average distance by whichrays miss the centroids of the pins 220-227 is more than ten microns,the refinement iterations continue. Each iteration of refinement maymore precisely determine positions and characteristics. If the clustererror is below a certain threshold (ten microns, for example), the pin220-227, detector array 160, and source 110 calculations are sufficient,and system 100 operation (e.g., imaging) may proceed. That is, thedetector position and source 110 motion may be used in reconstruction ofa medical diagnostic image through backprojection or other imagingmethod, for example.

While the answers obtained in the above calibration may not be perfect,the process may be iterated so that the solutions converge. In certainembodiments, calibration iterations converge to an answer in which anaverage ray will miss the centroid of its pin by no more than aboutthree microns. An image generated after such calibration is virtuallyfree of geometrically-caused streaks. Iterative calibration alsoprovides an accurate description in radius and angle of beam spot motionalong the target rings 140-143.

The following is a discussion of the mathematical method used to refinesystem 100 parameters and component configuration. For example, firstconsider a one dimensional case represented in FIG. 6. Assume there is avariable parameter “x” and a theoretical function “f” that operates onparameter x. For an observed empirical value, f(x₀), a value x₀ may bedetermined that will cause the function f to produce an observedempirical value f(x₀). Analysis begins with an initial guess x₁ which,when acted upon by the theoretical function, produces a value f(x₁). Ifthe derivatives of function “f”” may be calculated, a Taylor's seriesexpansion is performed about point x₁, $\begin{matrix}{{f\left( x_{0} \right)} = \left. {{f\left( x_{1} \right)} + {h \cdot \frac{\mathbb{d}f}{\mathbb{d}x}}} \middle| {}_{x_{1}}{{+ \frac{1}{2}}{h^{2} \cdot \frac{\mathbb{d}^{2}f}{\mathbb{d}^{2}x}}} \middle| {}_{x_{1}}{+ {\ldots\quad.}} \right.} & (1)\end{matrix}$

Since f(x₀) is a known, empirical value, solving for “h” may reveal howmuch to vary x₁ to produce x₀, the unknown quantity. Solving for h isimpractical, however, so the series is simplified to ignore second-orderand higher terms. The resulting equation is $\begin{matrix}{{{f\left( x_{0} \right)} \cong {f\left( x_{2} \right)}} = \left. {h_{1} \cdot \frac{\mathbb{d}f}{\mathbb{d}x}} \middle| {}_{x_{1}}. \right.} & (2)\end{matrix}$

Equation 2 may be solved for h₁, giving an approximate solution for animproved “x”,x ₂ =x ₁ +h ₁  (3).

Proceeding in this fashion, approximations may be refined to produce x₃,x₄, etc., each of which is closer to the desired value x₀. That is, theinput parameter may be refined until the theoretical function acting onthe input parameter produces the desired observed value.

However, rather than simply solving for a one-dimensional “x”, multipleparameters may be simultaneously optimized to produce a closetheoretical match to thousands of detector-pin “events” visible in thesinogram of the multipin phantom 200. The parameters include positionsof each pin 220-227, positions of the detector elements in the detectorarray 160, and the coefficients of the Fourier series describing themotion of the electron beam source in radius and angle, for example.Therefore, for a given detector element d and a given pin p, the error(difference between theoretical sample prediction q_(s) and measuredsample number q_(m)) may be written as $\begin{matrix}\begin{matrix}\left. {{q_{m}^{d,p} - q_{s}^{d,p}} \approx \frac{\partial q^{d,p}}{\partial R_{p}}} \middle| {}_{s}{{{\cdot \bigtriangledown}\quad R_{p}} + \frac{\partial q^{d,p}}{\partial\theta_{p}}} \middle| {}_{s}{{{\cdot \bigtriangledown}\quad\theta_{p}} +} \right. \\{\left. {\sum\limits_{j}^{ncoefs}\frac{\partial q^{d,p}}{\partial{rc}_{j}}} \middle| {}_{s}{{{\cdot \bigtriangledown}\quad{rc}_{j}} + {\sum\limits_{j}^{ncoefs}\frac{\partial q^{d,p}}{{\partial a}\quad c_{j}}}} \middle| {}_{s}{{\cdot \bigtriangledown}\quad a\quad c_{j}} \right.,}\end{matrix} & (4)\end{matrix}$where R_(p) represents the radius of pin P, θ_(p) represents the angleof pin P, rc_(j) represents the j^(th) radial coefficient of beammotion, and ac_(j) represents the j^(th) angular coefficient of beammotion.

In other words, the measured sample value of pin p in detector element dis roughly equal to the theoretical value plus the derivative of thesample function with respect to pin p's radius times ∇R, plus thederivative with respect to pin p's angle times ∇θ, plus the derivativesmultiplied by the deltas of the source coefficient terms, etc. A desiredresult of the calculation is the values of the deltas (“∇”) thatminimize the difference between measured pin sample values andtheoretical values obtained by applying the system model (“f”) to theparameter values (i.e., pin position, beam motion coefficients, etc.).

While equation (4) is one equation with multiple unknowns, creatingsimultaneous equations for all pins 220-227 seen by all detectorelements in the detector array 160 results in more equations thanunknowns. By casting the problem into a system of linear equations, anadjustment to the parameters (represented by the vector h) may bedetermined using singular value decomposition (SVD). SVD minimizes, in aleast-squares sense, the disagreement between theoretical sample valuesand the empirically measured values. Thus, equation (4) may begeneralized to a system of equations denoted by{right arrow over (E)}={right arrow over (h)}·P  (5),where {right arrow over (E)} represents the error or the differencebetween measurement and theory of each detector-pin combination, thevector {right arrow over (h)} denotes adjustments or deltas forindividual parameters to produce more accurate theoretical samplevalues, and P represents the matrix of partial derivatives of eachdetector-pin sample with respect to individual parameters.

The error vector {right arrow over (E)} may be represented as follows:detector 1detector 2 . . . detector n $\begin{matrix}{{\overset{\rightarrow}{E} = \left\lbrack {e_{1}^{1},e_{2}^{1},e_{3}^{1},\quad\ldots\quad,e_{npins}^{1},e_{2}^{2},e_{3}^{2},\quad\ldots\quad,e_{npins}^{n},\quad\ldots\quad,e_{1}^{n},e_{2}^{n},e_{3}^{n},\quad\ldots\quad,e_{npins}^{n}} \right\rbrack},} & (6)\end{matrix}$where e_(p)^(d)denotes a difference between empirical data and theory in the samplenumber of pin p as seen by detector d. The vector of parameter changesmay be represented as follows:{right arrow over (h)}=[ΔR _(p1), Δθ_(p1) , ΔR _(p2), Δθ_(p2) , . . . ,Δrc ₁ , Δrc ₂ , Δrc ₃ , . . . , Δac ₁ , Δac ₂ , Δac ₃, . . . ]  (7)where ΔR_(p) denotes a change in radius of pin p, Δθ_(p) represents achange in angle of pin p, Δ_(rc) represents a change in radial sourcecoefficient, and Δ_(ac) denotes a change in angular source coefficient.The matrix of derivatives P is shown below. In practice, pin positioncross terms may be set to zero, as a deviation in the position of onepin position has only a second order effect on another pin position.$\begin{matrix}{P = {\begin{bmatrix}{\frac{\partial q^{11}}{\partial R_{p1}}\frac{\partial q^{11}}{\partial\theta_{p1}}\frac{\partial q^{11}}{\partial R_{p2}}\frac{\partial q^{11}}{\partial\theta_{p2}}} & \ldots & {\frac{\partial q^{11}}{\partial{rc}_{1}}\frac{\partial q^{11}}{\partial{rc}_{2}}} & \ldots & {\frac{\partial q^{11}}{\partial{ac}_{1}}\frac{\partial q^{11}}{\partial{ac}_{2}}} & \ldots \\{\frac{\partial q^{12}}{\partial R_{p1}}\frac{\partial q^{12}}{\partial\theta_{p1}}\frac{\partial q^{12}}{\partial R_{p2}}\frac{\partial q^{12}}{\partial\theta_{p2}}} & \ldots & {\frac{\partial q^{12}}{\partial{rc}_{1}}\frac{\partial q^{12}}{\partial{rc}_{2}}} & \ldots & {\frac{\partial q^{12}}{\partial{ac}_{1}}\frac{\partial q^{12}}{\partial{ac}_{2}}} & \ldots \\{\frac{\partial q^{13}}{\partial R_{p1}}\frac{\partial q^{13}}{\partial\theta_{p1}}\frac{\partial q^{13}}{\partial R_{p2}}\frac{\partial q^{13}}{\partial\theta_{p2}}} & \ldots & {\frac{\partial q^{13}}{\partial{rc}_{1}}\frac{\partial q^{13}}{\partial{rc}_{2}}} & \ldots & {\frac{\partial q^{13}}{\partial{ac}_{1}}\frac{\partial q^{13}}{\partial{ac}_{2}}} & \ldots \\\quad & \ldots & \quad & \ldots & \quad & \ldots \\{\frac{\partial q^{21}}{\partial R_{p1}}\frac{\partial q^{21}}{\partial\theta_{p1}}\frac{\partial q^{21}}{\partial R_{p2}}\frac{\partial q^{21}}{\partial\theta_{p2}}} & \ldots & {\frac{\partial q^{21}}{\partial{rc}_{1}}\frac{\partial q^{21}}{\partial{rc}_{2}}} & \ldots & {\frac{\partial q^{21}}{\partial{ac}_{1}}\frac{\partial q^{21}}{\partial{ac}_{2}}} & \ldots \\{\frac{\partial q^{22}}{\partial R_{p1}}\frac{\partial q^{22}}{\partial\theta_{p1}}\frac{\partial q^{22}}{\partial R_{p2}}\frac{\partial q^{22}}{\partial\theta_{p2}}} & \ldots & {\frac{\partial q^{22}}{\partial{rc}_{1}}\frac{\partial q^{22}}{\partial{rc}_{2}}} & \ldots & {\frac{\partial q^{22}}{\partial{ac}_{1}}\frac{\partial q^{22}}{\partial{ac}_{2}}} & \ldots \\{\frac{\partial q^{23}}{\partial R_{p1}}\frac{\partial q^{23}}{\partial\theta_{p1}}\frac{\partial q^{23}}{\partial R_{p2}}\frac{\partial q^{23}}{\partial\theta_{p2}}} & \ldots & {\frac{\partial q^{23}}{\partial{rc}_{1}}\frac{\partial q^{23}}{\partial{rc}_{2}}} & \ldots & {\frac{\partial q^{23}}{\partial{ac}_{1}}\frac{\partial q^{23}}{\partial{ac}_{2}}} & \ldots \\\quad & \ldots & \quad & \ldots & \quad & \ldots \\{\frac{\partial q^{n1}}{\partial R_{p1}}\frac{\partial q^{n1}}{\partial\theta_{p1}}\frac{\partial q^{n1}}{\partial R_{p2}}\frac{\partial q^{n1}}{\partial\theta_{p2}}} & \ldots & {\frac{\partial q^{n1}}{\partial{rc}_{1}}\frac{\partial q^{n1}}{\partial{rc}_{2}}} & \ldots & {\frac{\partial q^{n1}}{\partial{ac}_{1}}\frac{\partial q^{n1}}{\partial{ac}_{2}}} & \ldots \\{\frac{\partial q^{n2}}{\partial R_{p1}}\frac{\partial q^{n2}}{\partial\theta_{p1}}\frac{\partial q^{n2}}{\partial R_{p2}}\frac{\partial q^{n2}}{\partial\theta_{p2}}} & \ldots & {\frac{\partial q^{n2}}{\partial{rc}_{1}}\frac{\partial q^{n2}}{\partial{rc}_{2}}} & \ldots & {\frac{\partial q^{n2}}{\partial{ac}_{1}}\frac{\partial q^{n2}}{\partial{ac}_{2}}} & \ldots \\{\frac{\partial q^{n3}}{\partial R_{p1}}\frac{\partial q^{n3}}{\partial\theta_{p1}}\frac{\partial q^{n3}}{\partial R_{p2}}\frac{\partial q^{n3}}{\partial\theta_{p2}}} & \ldots & {\frac{\partial q^{n3}}{\partial{rc}_{1}}\frac{\partial q^{n3}}{\partial{rc}_{2}}} & \ldots & {\frac{\partial q^{n3}}{\partial{ac}_{1}}\frac{\partial q^{n3}}{\partial{ac}_{2}}} & \ldots \\\quad & \ldots & \quad & \ldots & \quad & \ldots\end{bmatrix}{\begin{matrix}\quad & \quad \\{{pin}\quad 1} & \quad \\\quad & \quad \\{{pin}\quad 2} & {{detector}\quad 1} \\\quad & \quad \\{{pin}\quad 3} & \quad \\\quad & \quad \\\quad & \quad \\{{pin}\quad 1} & \quad \\\quad & \quad \\{{pin}\quad 2} & {{detector}\quad 2} \\\quad & \quad \\\quad & \quad \\{{pin}\quad 3} & \quad \\\quad & \quad \\\quad & \quad \\{{pin}\quad 1} & \quad \\\quad & \quad \\{{pin}\quad 2} & {{detector}\quad n} \\\quad & \quad \\{{pin}\quad 3} & \quad \\\quad & \quad \\\quad & \quad\end{matrix}.\begin{matrix}{\quad{{pin}\quad{positions}}} & {\quad{{rad}.\quad{coeffs}.}} & {\quad{{ang}.\quad{coeffs}.}} \\\quad & \quad & \quad\end{matrix}}}} & (8)\end{matrix}$The matrix P includes a number of rows equal to the number of detectorelements n in the detector array 160 in the system 100 multiplied by thenumber n of pins 220-227. The number of columns in the matrix P is equalto twice the number n of pins 220-227 (one term for each radius, oneterm for each angle) plus the number of source coefficients. The firstset of columns represents derivative terms for the pin positions,varying the radius and angle of each pin according to sample number. Thesecond set of columns varies the radius coefficients of the sourceelectron beam. The third set of columns varies the angle coefficients ofthe source.

Calculation of the derivative terms may be accomplished numerically.Once the equation E=h*P is set up, the solution involves using asingular value decomposition (SVD) algorithm to solve for h. Values inthe vector h may be added to the initial parameters to provide a moreaccurate list of pin 220-227 positions and source 110 coefficients.Improved detector element positions may also be calculated. Solving fordetector element positions by adding detector element positions to thesystem of equations results in too large of a solution space for currentoff-the-shelf computers. Thus, a separate “clustering” method may beused in which detector element positions are solved for individually.For each detector element, the source coefficients are evaluated at thetimes of each pin 220-227 sighting (yielding the source 110 positions).Rays may be drawn from the target 140-143 through the pins 220-227. Apoint of convergence is calculated. The detector element position isupdated to the point of convergence, barring errors or unlikely results.The process of setting up the system of equations, solving the system,and clustering of detector elements may then be repeated until asufficient answer is obtained.

In certain embodiments, motion and other characteristics of the energybeam may be modified based on the above described calibration method.For example, iterative calibration of the detector array 160 and energysource 110 is performed, as described above in reference to FIGS. 1, 2and 3. Then, beam spot motion information is used to adjust currentsapplied to the deflection coils 130 coils. A complete set of coilcurrents for a scan is called a “tune”.

FIG. 7 illustrates an electron beam tuning system 700 formed inaccordance with an embodiment of the present invention. The system 700includes a radial beam correction module 780 and an angular beamadjustment module 790. The radial beam correction module 780 and theangular beam adjustment module 790 may be separate units or may becombined in a single unit. The radial beam correction module 780 and theangular beam adjustment module 790 may be embodied in hardware and/or insoftware. The system 700 may be used in conjunction with an electronsource 710, a focusing coil 720, deflection coils 730, target rings740-743, a DAS 750, a reconstruction system 755, a detector array 760,an object positioner 770, and a multipin phantom 775. The electronsource 710, focusing coil 720, deflection coil 730, target rings740-743, DAS 750, reconstruction system 755, detector array 760, objectpositioner 770, and multipin phantom 775 are similar to the componentsdescribed above in relations to FIG. 1 and FIG. 2.

In operation, tuning is similar to calibration described above. Themultipin phantom 775 is placed on the object positioner 770 withoutparticular regard to accuracy. A scan is acquired. Then, the iterativecomputations previously described are performed to characterize themotion of the beam spot along the target rings 140-143.

Once beam spot and/or electron beam motion have been determined, coilcurrents may be adjusted to optimize beam spot and/or electron beammovement. Coil currents for the deflection coil are stored as a seriesof deflection update blocks (DUBs). A DUB represents a single “quantum”of coil currents sent to each deflection coil. In certain embodiments, aDUB is stored for every twenty microseconds. Thus, a single deflectionbuffer may contain thousands of DUBs.

In correcting radial fluctuations of the motion of the beam spot alongthe target rings 140-143, the radius of the beam spot is examined at thetime of each DUB. If the radius is too large (too much deflection), thedipole currents in the deflection coil are decreased by a scale factorproportional to the size of the deviation from an ideal tune. If theradius is too small (not enough deflection), the dipole currents areincreased by a scale factor proportional to the size of the deviationfrom an ideal tune. By going through each DUB and scaling the dipolecurrents, a tune that is substantially flatter and closer to an idealtune than the original tune may be obtained. The above process may beiterated (rescan the multipin phantom 775 with the new tune, redo themultipin phantom 775 calibration, and re-correct the deflection buffers)to produce a set of coil currents with a desired radial flatness.

The angular motion of the electron beam may also be adjusted usinginformation from the multipin phantom 775. An optimal tune produces abeam spot that moves with a constant angular velocity. An initial tunemay have angular accelerations and decelerations. Deviations from thedesired angular velocity may be flattened out on a DUB-by-DUB basis.Each DUB corresponds to a specified time; hence the desired angularposition of the beam spot for each DUB is known. The actual angularposition at a given time is contained in a beam spot position filecalculated using the multipin phantom 775. Although the beam spot goesthrough all the correct angles, the beam spot may not be at the correctangle at the correct time.

By searching through the existing DUBs and beam spot position file, coilcurrents may be found that will place the electron beam at the desiredposition for any given DUB. These currents are then interpolated andloaded into the DUB that is being optimized. For example, assume thatthe DUB at 25 milliseconds is the one being optimized. It may be thatthe desired location of the beam spot at this time is the 6 o'clockposition. However, the actual beam spot may be at the 6 o'clock positionat a different time, for example t=24.985 ms. In that case, the coilcurrents in the two DUBS spanning 24.985 ms would be linearlyinterpolated and placed in the DUB at 25 ms. Linear interpolation orcombination will help ensure that the beam spot will be at the 6 o'clockposition at 25 ms into the scan.

Linear combination is performed for every DUB in the deflection buffer.Through linear combination, the angular deviations are “flattened,” anda constant angular velocity is approached. In some embodiments, theflattening process is iterated to approach the desired angular velocity.Physical limitations of the deflection coil 730 and focusing coil 720and effects of the previously described radial modifications beingperformed along with the angular modifications may result in iteration.

FIG. 8 illustrates a flow diagram 800 for a method for adjusting anelectron beam used in accordance with an embodiment of the presentinvention. First, pin positions, detector element positions, andelectron beam motion parameters are determined through estimation andrefinement according to steps 310-370 described above. When detectorelement positions and electron beam motion have been computed, theelectron beam may be adjusted as described below.

Electron beam and beam spot motion parameters, as well as otherparameters, such as pin positions and detector element positions, may bestored in a file. At step 375, the file, such as the beam spot motionfile, may be loaded or retrieved in the system 700 for use in adjustingthe electron beam.

At step 380, currents for the deflection coils 730 are loaded from aseries of deflection update blocks (DUBs). Then, at step 385, the radiusof the electron beam spot is examined at the time of each DUB. If theradius is too large (indicating too much deflection, for example), thedipole currents in the deflection coil are decreased by a scale factorproportional to the size of the deviation from an ideal coil current ortune. If the radius is too small (indicating not enough deflection, forexample), the dipole currents are increased by a scale factorproportional to the size of the deviation from an ideal tune.

Next, at step 390, DUBS are adjusted to put the beam at a proper angleas a function of time. Using the search and interpolation methoddescribed above, the coil currents are modified to make the beam spotsweep along the targets 140-143 with the correct constant angularvelocity.

Finally, at step 395, the adjusted coil current values are stored. Theadjusted coil currents aim and focus the electron beam in theelectromagnetic focusing coil 20 and deflection coils 730 to strike adesired position on the target rings 740-743 at a desired time. Theabove steps may be repeated as necessary to adjust the electron beam.

While the invention has been described with reference to certainembodiments, it will be understood by those skilled in the art thatvarious changes may be made and equivalents may be substituted withoutdeparting from the scope of the invention. In addition, manymodifications may be made to adapt a particular situation or material tothe teachings of the invention without departing from its scope.Therefore, it is intended that the invention not be limited to theparticular embodiment disclosed, but that the invention will include allembodiments falling within the scope of the appended claims.

1. A method for calibrating an imagine system having an array ofdetector elements arranged with respect to a reference position andhaving an energy source moving in a pattern to irradiate the array ofdetector elements, the method comprising: initiating estimated detectorpositions for the array of detector elements and an estimated motionpattern for the energy source, said estimated detector positions andmotion pattern being defined with respect to a reference position in theimaging system; scanning a phantom having pins located at positions inthe phantom; calculating estimated pin positions for the pins in thephantom, with respect to the reference position, based on at least oneof said estimated detector positions and motion pattern; and modifyingat least one of said estimated detector positions and motion patternbased on at least two of said estimated detector positions, motionpattern and pin positions.
 2. The method of claim 1, further comprisingdetermining an amount of error in at least one of said estimateddetector positions, motion pattern and pin positions; and, when theamount of error exceeds a threshold, repeating said calculating andmodifying steps.
 3. The method of claim 1, further comprising: repeatingsaid calculating and modifying steps at least once to obtain first andsecond estimated detector positions, motion pattern and pin positions;and calculating an amount of error between said first and secondestimated detector positions, motion pattern and pin positions.
 4. Themethod of claim 1, further comprising: drawing rays between associatedpoints along said estimated motion pattern of the energy source and saidestimated detector positions; and utilizing points of intersectionbetween the rays to calculate said estimated pin positions.
 5. Themethod of claim 1, further comprising: determining actual pin positionsfrom the scan of the phantom; and calculating a difference between saidestimated and actual pin positions.
 6. The method of claim 1, furthercomprising: determining actual pin positions: calculating a pin errorrepresenting an amount by which said estimated pin positions differedfrom said actual pin positions; and modifying said estimated detectorpositions based on the pin error.
 7. The method of claim 1, furthercomprising: determining actual pin positions; calculating a pin errorrepresenting an amount by which said estimated pin positions differedfrom said actual pin positions; and modifying said estimated motionpattern for the energy source based on the pin error.
 8. The method ofclaim 1, wherein said motion pattern of the energy source comprises anarc.
 9. The method of claim 1, wherein said modifying step furthercomprises computing an error vector E=h*P, wherein E represents an errorassociated with at least one of said estimated detector positions,motion pattern and pin positions, h denotes adjustments to produce moreaccurate estimated detector positions, motion pattern and pin positionsand P represents a matrix of derivatives for detector-phantom pinsamples with respect to said detector positions, motion pattern and pinpositions.
 10. The method of claim 1, wherein the phantom is positionedin the imaging system independent of the reference position.
 11. Asystem for improved calibration of a diagnostic imaging system, saidsystem comprising: an array of detector elements arranged with respectto a reference position; an energy source moving in a pattern toirradiate said array of detector elements; a phantom having pins locatedat positions in said phantom; and a reconstruction system calculatingestimated pin positions for said pins in said phantom, with respect tosaid reference position, based on at least one of estimated detectorpositions and estimated motion pattern of said energy source, saidreconstruction system modifying at least one of the estimated detectorpositions and motion pattern based on at least two of the estimateddetector positions, motion pattern, and pin positions.
 12. The system ofclaim 11, wherein said reconstruction system modifies at least one ofthe estimated detector positions and motion pattern by computing anerror vector E=h*P, wherein E represents an error associated with atleast one of the estimated detector positions, motion pattern and pinpositions, h denotes adjustments to produce more accurate estimateddetector positions, motion pattern and pin positions and P represents amatrix of derivatives for detector-phantom pin samples with respect tothe detector positions, motion pattern and pin positions.
 13. The systemof claim 11, wherein the motion pattern of said energy source comprisesan arc.
 14. The system of claim 11, wherein said reconstruction systemdetermines an amount of error in at least one of the estimated detectorpositions, motion pattern; and pin positions, and, when the amount oferror exceeds a threshold, said reconstruction system repeatscalculating and modifying at least one of estimated detector positions,motion pattern and pin positions.